The connection between generalized convexity and symmetry has been studied by many authors in recent years. Due to this strong connection, have arisen as a new topic the subject of inequalities. In paper, we introduce concept interval-valued preinvex functions on coordinates rectangle from plane prove Hermite–Hadamard type inclusions for coordinates. Further, establish product two coordinated f...

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued ma...

The goal of this study is to create new variations the well-known Hermite–Hadamard inequality (HH-inequality) for preinvex interval-valued functions (preinvex I-V-Fs). We develop several additional inequalities class whose product I-V-Fs. findings described here would be generalizations those found in previous studies. Finally, we obtain Hermite–Hadamard–Fejér with support functions. Some and c...

The Fefferman-Stein vector-valued maximal function inequality is proved for spaces of homogeneous type. The approach taken here is based on the theory of vector-valued Calderón-Zygmund singular integral theory in this context, which is appropriately developed.